Unlock Bonus Stages in the Demo
Instead of pressing [A]+[B] at the main menu, press and hold [1]+[2] when pressing [A]+[B] to access two additional stages.

Unlock Hidden Character
Get all 120 stars, and then return to Rosalina (on the Comet Observatory). Request to fight Bowser again. Finish the credits and you will get a message saying that Luigi is now playable.

Homing Attack
Spin in mid-air and press [Z] to do a homing attack on the nearest enemy or breakable item.

Death Count
The Grand Finale Galaxy (a secret galaxy that can be unlocked after 120 Stars are gathered with both Mario and Luigi) holds another secret -- once this final Star from the stage is acquired with both Mario and Luigi, you will be able to see your death count on your save file. You can now see how many times you died while playing the game with both Mario and Luigi.

Hints

Zelda Rupee
Once you have unlocked the Rolling Gizmo Galaxy as one of the trial galaxies go into it's level. Walk past the ball and get on top of the metal cubes. Do some fancy wall jumping onto the bridge. Once on top, go to the edge and pan the camera down. You will see a Zelda Rupee made out of star bits!